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Oscillation theorems for second-order quasilinear neutral functional differential equations. (English) Zbl 1251.34083

Summary: New oscillation criteria are established for the second-order nonlinear neutral functional differential equations \[ (r(t)|z'(t)|^{\alpha -1} z'())' + f(t, x[\sigma(t)]) = 0, \] where \(t \geq t_0\), \(z(t) = x(t) + p(t)x(\tau(t))\), \(p \in C^1([t_0, \infty),[0, \infty))\) and \(\alpha \geq 1\). Some examples are provided.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
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